One of the issues that usually comes up at some point during any extended discussion of the fundamentals of the Reciprocal System of theory is what the writers of detective stories would probably call The Case of the Colliding Photons. This perennial stumbling block that troubles so many of those who try to follow the development of the theoretical structure was given some attention during the conference in Minneapolis, but inasmuch as there were still a number of question marks in the air when it became necessary to turn to other matter; a full review of the situation is no doubt in order.

As brought out in the publications which describe the theory of a universe of motion, the natural system of reference to which such a universe conforms moves outward at unit speed (the speed of light) with respect to a stationary coordinate system of reference. Any object which has no capability of independent motion, and is not acted upon by any external forces, remains stationary with respect to the natural system of reference, and it therefore moves outward from all other such objects at unit speed. It 1s not possible for two such objects to meet.

Atoms of matter are likewise carried outward away from each other by the outward progression of the natural reference system, in the same manner as the photons, but these atoms do have independent motions of their own. These atomic notions are inward, in opposition to the Progression, and if the atoms are within the applicable gravitational limits, the magnitude of the inward notion is greater than that of the outward progression. The total number of atoms subject to a system of interrelated gravitational motions constitutes what we call a gravitationally hound system. Atoms within such a system can collide under appropriate conditions.

Photons emitted by atoms in a gravitationally bound system have no capability of independent motion, but they are subject to external forces (that is, to motions of external origin) inasmuch as they participate in whatever motions the emitting aggregates of atoms may have had when the emission occurred. At the instant of emission, the photon is moving with the aggregate, and it has no mechanism whereby it can eliminate that motion. The progression therefore takes place outward in a reference frame defined by the emitting aggregate. Each such aggregate is the center of a sphere of radiation, and in a gravitationally bound system the spheres are coexistent. Photons of this radiation may therefore collide with other photons emitted within the bound system, or with atoms of that system.

Some objections have been raised to this explanation of the colliding photon situation on the ground that the addition of the unit speed of the photon to the preexistent speed of the emitting aggregate on that foregoing basis conflicts with the established fact that the speed of light is independent of the speed of The emitting object. However, this objection is based on an erroneous assumption. It assumes that the changes in the relative spatial positions of the photons are determined by the relative speeds, which is not true

I have discussed the general question of motion at high speeds at some length in most of my books (see, for instance page 30 of *Quasars and Pulsars*). In the illustration that I have generally used, I consider two photons emitted simultaneously from a common stationary source in opposite directions. At the end of one unit of clock time photon a has reached point A, one spatial unit distant from the point of emission, which we will designate as O. This distance OA in the stationary reference system is an absolute magnitude that is totally independent of anything that any other photon may do. During the same interval of clock time photon b moves to point B one unit of spate distant from O in the direction opposite to A. The distance OB in the stationary reference system is also an absolute magnitude totally independent of anything that may happen to any other photon. Thus, during one unit of clock time the spatial separation between photons a and b in a stationary three-dimensional frame of reference, which was originally zero has increased to two units. This is a simple objective fact that does not depend in any way on the particular theoretical system in whose context the situation is viewed.

If we replace photon b by a material object that moves with a speed of natural unit, the separation at the end of one unit of clock time is 1½ spatial units. If we substitute a stationary object for photon b, the resulting separation is only I spatial unit. In all of these cases, the separation and consequently the time rate of change of the relative spatial positions of the moving objects is determined by a combination of the individual speeds involved. But both conventional theory and the Reciprocal System agree that the speed of a relative to b is unity, the speed of light, in all three examples. This the measured speed of the photon does not determine the relative spatial position that it will occupy at any particular time.

This may seem paradoxical, but the explanation is that any excess of the rate of spatial separation over one unit of space per unit of time is offset by motion in three-dimensional time, and therefore has no effect on the relative speed. The same considerations apply where photons are emitted from a moving object. Although the measured speed of the photon is simply the magnitude of the progression of the natural reference system, and is independent of the motion of the emitting object, the presumed conflict between the constant speed of light and the photon collisions is therefore without foundation.